Code

Memory limit: 32 MB

A binary tree can either be empty or consist of one vertex, with two trees linked to it. These two trees are called a left and a right subtree. In each vertex there is one letter from the English alphabet. The vertex which is not a subtree of any vertex, is called a root. We say that a tree is a Binary Search Tree (BST) if for each vertex the following condition is satisfied: all letters in the left subtree precede in alphabetical order the letter in the root, and all letters from the right subtree follow the letter in the root. A code of a BST is:

• either an empty string (containing 0 letters) when the tree is empty
• or a string beginning with the letter from the root, followed by the code of the left subtree, followed by the code of the right subtree.

-code

Example

There are exactly fourteen 4-vertex BSTs. These are (in alphabetical order):

The string badc is the (7,4)-code and it corresponds to the BST printed below:

Task

Write a program which:

• reads the numbers and from the standard input,
• finds the -code,
• writes it to the standard output.

Input

In the first and only line of the standard input there are exactly two positive integers and , separated by a single space, . The number is not greater than the number of codes of BST with vertices.

Output

In the first and only line of the standard output there should be exactly one word (written in small letters) being the -code.

Example

For the input data:

11 4

the correct result is:

dacb

Task author: Wojciech Guzicki.